Cross-multiply (or, in other words, multiply both sides by (2+x)*(x+1)) to rid of the denominators. You will get (1-x)*(x+1) = (x-2)*(2+x). Simplify: 1 - x^2 = x^2 - 4, 1 + 4 = x^2 + x^2, 5 = 2x^2, x^2 = ---> x = +/- = +/- . Answer. x = +/- .